TSTP Solution File: SEU668^2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU668^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 03:38:57 EDT 2024

% Result   : Theorem 12.02s 3.39s
% Output   : Refutation 12.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  102 (  46 unt;  17 typ;   4 def)
%            Number of atoms       :  235 (  94 equ;   0 cnn)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  804 (  90   ~;  61   |;  18   &; 602   @)
%                                         (   0 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   78 (  78   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;  11 con; 0-3 aty)
%            Number of variables   :  276 (  52   ^ 211   !;  13   ?; 276   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(dsetconstrER_type,type,
    dsetconstrER: $o ).

thf(dsetconstrER_def,definition,
    ( dsetconstrER
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( B @ C ) ) ) ) ).

thf(kpair_type,type,
    kpair: $i > $i > $i ).

thf(cartprod_type,type,
    cartprod: $i > $i > $i ).

thf(setukpairinjL_type,type,
    setukpairinjL: $o ).

thf(setukpairinjL_def,definition,
    ( setukpairinjL
    = ( ! [A: $i,B: $i,C: $i,D: $i] :
          ( ( ( kpair @ A @ B )
            = ( kpair @ C @ D ) )
         => ( A = C ) ) ) ) ).

thf(setukpairinjR_type,type,
    setukpairinjR: $o ).

thf(setukpairinjR_def,definition,
    ( setukpairinjR
    = ( ! [A: $i,B: $i,C: $i,D: $i] :
          ( ( ( kpair @ A @ B )
            = ( kpair @ C @ D ) )
         => ( B = D ) ) ) ) ).

thf(dpsetconstr_type,type,
    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).

thf(dpsetconstr_def,definition,
    ( dpsetconstr
    = ( ^ [A: $i,B: $i,C: $i > $i > $o] :
          ( dsetconstr @ ( cartprod @ A @ B )
          @ ^ [D: $i] :
            ? [E: $i] :
              ( ( in @ E @ A )
              & ? [F: $i] :
                  ( ( in @ F @ B )
                  & ( C @ E @ F )
                  & ( D
                    = ( kpair @ E @ F ) ) ) ) ) ) ) ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i > $i > $o ).

thf(sk4_type,type,
    sk4: $i ).

thf(sk5_type,type,
    sk5: $i ).

thf(sk6_type,type,
    sk6: $i > $i > $i ).

thf(sk7_type,type,
    sk7: $i > $i > $i ).

thf(sk8_type,type,
    sk8: $i ).

thf(sk9_type,type,
    sk9: $i ).

thf(1,conjecture,
    ( dsetconstrER
   => ( setukpairinjL
     => ( setukpairinjR
       => ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
            ( ( in @ D @ A )
           => ! [E: $i] :
                ( ( in @ E @ B )
               => ( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
                 => ( C @ D @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrERa) ).

thf(2,negated_conjecture,
    ~ ( dsetconstrER
     => ( setukpairinjL
       => ( setukpairinjR
         => ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
              ( ( in @ D @ A )
             => ! [E: $i] :
                  ( ( in @ E @ B )
                 => ( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
                   => ( C @ D @ E ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( B @ C ) )
     => ( ! [A: $i,B: $i,C: $i,D: $i] :
            ( ( ( kpair @ A @ B )
              = ( kpair @ C @ D ) )
           => ( A = C ) )
       => ( ! [A: $i,B: $i,C: $i,D: $i] :
              ( ( ( kpair @ A @ B )
                = ( kpair @ C @ D ) )
             => ( B = D ) )
         => ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
              ( ( in @ D @ A )
             => ! [E: $i] :
                  ( ( in @ E @ B )
                 => ( ( in @ ( kpair @ D @ E )
                      @ ( dsetconstr @ ( cartprod @ A @ B )
                        @ ^ [F: $i] :
                          ? [G: $i] :
                            ( ( in @ G @ A )
                            & ? [H: $i] :
                                ( ( in @ H @ B )
                                & ( C @ G @ H )
                                & ( F
                                  = ( kpair @ G @ H ) ) ) ) ) )
                   => ( C @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( B @ C ) )
     => ( ! [A: $i,B: $i,C: $i] :
            ( ? [D: $i] :
                ( ( kpair @ A @ B )
                = ( kpair @ C @ D ) )
           => ( A = C ) )
       => ( ! [A: $i,B: $i,C: $i,D: $i] :
              ( ( ( kpair @ A @ B )
                = ( kpair @ C @ D ) )
             => ( B = D ) )
         => ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
              ( ( in @ D @ A )
             => ! [E: $i] :
                  ( ( in @ E @ B )
                 => ( ( in @ ( kpair @ D @ E )
                      @ ( dsetconstr @ ( cartprod @ A @ B )
                        @ ^ [F: $i] :
                          ? [G: $i] :
                            ( ( in @ G @ A )
                            & ? [H: $i] :
                                ( ( in @ H @ B )
                                & ( C @ G @ H )
                                & ( F
                                  = ( kpair @ G @ H ) ) ) ) ) )
                   => ( C @ D @ E ) ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(7,plain,
    ( in @ ( kpair @ sk4 @ sk5 )
    @ ( dsetconstr @ ( cartprod @ sk1 @ sk2 )
      @ ^ [A: $i] :
        ? [B: $i] :
          ( ( in @ B @ sk1 )
          & ? [C: $i] :
              ( ( in @ C @ sk2 )
              & ( sk3 @ B @ C )
              & ( A
                = ( kpair @ B @ C ) ) ) ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( B @ C ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(63,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( ( in @ ( kpair @ sk4 @ sk5 )
          @ ( dsetconstr @ ( cartprod @ sk1 @ sk2 )
            @ ^ [D: $i] :
              ? [E: $i] :
                ( ( in @ E @ sk1 )
                & ? [F: $i] :
                    ( ( in @ F @ sk2 )
                    & ( sk3 @ E @ F )
                    & ( D
                      = ( kpair @ E @ F ) ) ) ) ) )
       != ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,10]) ).

thf(64,plain,
    ? [A: $i] :
      ( ( in @ A @ sk1 )
      & ? [B: $i] :
          ( ( in @ B @ sk2 )
          & ( sk3 @ A @ B )
          & ( ( kpair @ sk4 @ sk5 )
            = ( kpair @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( cartprod @ sk1 @ sk2 )),bind(B,$thf( ^ [D: $i] : ? [E: $i] : ( ( in @ E @ sk1 ) & ? [F: $i] : ( ( in @ F @ sk2 ) & ( sk3 @ E @ F ) & ( D = ( kpair @ E @ F ) ) ) ) )),bind(C,$thf( kpair @ sk4 @ sk5 ))]]) ).

thf(69,plain,
    in @ sk9 @ sk2,
    inference(cnf,[status(esa)],[64]) ).

thf(5,plain,
    ~ ( sk3 @ sk4 @ sk5 ),
    inference(cnf,[status(esa)],[4]) ).

thf(19,plain,
    ! [F: $i,E: $i > $o,D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( E @ F )
      | ( ( B @ C )
       != ( in @ F @ ( dsetconstr @ D @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10,10]) ).

thf(34,plain,
    ! [E: $i > $i > $o,D: $i > $i,C: $i > $i,B: $i,A: $i] :
      ( ~ ( in @ B
          @ ( dsetconstr @ A
            @ ^ [F: $i] : ( in @ ( C @ F ) @ ( dsetconstr @ ( D @ F ) @ ( E @ F ) ) ) ) )
      | ( E @ B @ ( C @ B ) ) ),
    inference(pre_uni,[status(thm)],[19:[bind(A,$thf( A )),bind(B,$thf( ^ [J: $i] : ( in @ ( G @ J ) @ ( dsetconstr @ ( I @ J ) @ ( J @ J ) ) ) )),bind(C,$thf( C )),bind(D,$thf( I @ C )),bind(E,$thf( J @ C )),bind(F,$thf( G @ C ))]]) ).

thf(37,plain,
    ! [E: $i > $i > $o,D: $i > $i,C: $i > $i,B: $i,A: $i] :
      ( ~ ( in @ B
          @ ( dsetconstr @ A
            @ ^ [F: $i] : ( in @ ( C @ F ) @ ( dsetconstr @ ( D @ F ) @ ( E @ F ) ) ) ) )
      | ( E @ B @ ( C @ B ) ) ),
    inference(simp,[status(thm)],[34]) ).

thf(9,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( kpair @ A @ B )
       != ( kpair @ C @ D ) )
      | ( B = D ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(12,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( kpair @ A @ B )
       != ( kpair @ C @ D ) )
      | ( B = D ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(13,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( kpair @ A @ B )
       != ( kpair @ C @ D ) )
      | ( B = D ) ),
    inference(simp,[status(thm)],[12]) ).

thf(14,plain,
    ! [B: $i,A: $i] :
      ( ( sk6 @ A @ ( kpair @ A @ B ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(kpair),[sk6])]) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B
          @ ( dsetconstr @ A
            @ ^ [C: $i] : $false ) )
      | $false ),
    inference(prim_subst,[status(thm)],[10:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : $false ))]]) ).

thf(46,plain,
    ! [B: $i,A: $i] :
      ~ ( in @ B
        @ ( dsetconstr @ A
          @ ^ [C: $i] : $false ) ),
    inference(simp,[status(thm)],[28]) ).

thf(6,plain,
    in @ sk5 @ sk2,
    inference(cnf,[status(esa)],[4]) ).

thf(18,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( ( B @ C )
       != ( sk3 @ sk4 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[10,5]) ).

thf(33,plain,
    ! [A: $i] :
      ~ ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) ),
    inference(pre_uni,[status(thm)],[18:[bind(A,$thf( A )),bind(B,$thf( sk3 @ sk4 )),bind(C,$thf( sk5 ))]]) ).

thf(105,plain,
    ! [A: $i] :
      ( ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) )
     != ( in @ sk5 @ sk2 ) ),
    inference(paramod_ordered,[status(thm)],[6,33]) ).

thf(110,plain,
    ! [A: $i] :
      ( ( sk5 != sk5 )
      | ( ( dsetconstr @ A @ ( sk3 @ sk4 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[105]) ).

thf(121,plain,
    ! [A: $i] :
      ( ( dsetconstr @ A @ ( sk3 @ sk4 ) )
     != sk2 ),
    inference(simp,[status(thm)],[110]) ).

thf(20,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( ( in @ sk5 @ sk2 )
       != ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6,10]) ).

thf(29,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( sk5 != C )
      | ( ( dsetconstr @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[20]) ).

thf(47,plain,
    ! [B: $i > $o,A: $i] :
      ( ( B @ sk5 )
      | ( ( dsetconstr @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[29]) ).

thf(32,plain,
    ! [A: $i] :
      ~ ( in @ sk4
        @ ( dsetconstr @ A
          @ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) ),
    inference(pre_uni,[status(thm)],[18:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ( sk3 @ D @ sk5 ) )),bind(C,$thf( sk4 ))]]) ).

thf(719,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( ( dsetconstr @ A @ B )
       != sk2 )
      | ( ( B @ sk5 )
       != ( in @ sk4
          @ ( dsetconstr @ C
            @ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47,32]) ).

thf(732,plain,
    ! [B: $i > $i,A: $i] :
      ( ( dsetconstr @ A
        @ ^ [C: $i] :
            ( in @ sk4
            @ ( dsetconstr @ ( B @ C )
              @ ^ [D: $i] : ( sk3 @ D @ C ) ) ) )
     != sk2 ),
    inference(pre_uni,[status(thm)],[719:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ sk4 @ ( dsetconstr @ ( F @ E ) @ ^ [F: $i] : ( sk3 @ F @ E ) ) ) )),bind(C,$thf( F @ sk5 ))]]) ).

thf(757,plain,
    ! [B: $i > $i,A: $i] :
      ( ( dsetconstr @ A
        @ ^ [C: $i] :
            ( in @ sk4
            @ ( dsetconstr @ ( B @ C )
              @ ^ [D: $i] : ( sk3 @ D @ C ) ) ) )
     != sk2 ),
    inference(simp,[status(thm)],[732]) ).

thf(25,plain,
    ! [D: $i > $o,C: $i > $o,B: $i,A: $i] :
      ( ~ ( in @ B
          @ ( dsetconstr @ A
            @ ^ [E: $i] :
                ( ( C @ E )
                | ( D @ E ) ) ) )
      | ( C @ B )
      | ( D @ B ) ),
    inference(prim_subst,[status(thm)],[10:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( ( D @ F ) | ( E @ F ) ) ))]]) ).

thf(43,plain,
    ! [D: $i > $o,C: $i > $o,B: $i,A: $i] :
      ( ( C @ B )
      | ( D @ B )
      | ~ ( in @ B
          @ ( dsetconstr @ A
            @ ^ [E: $i] :
                ( ( C @ E )
                | ( D @ E ) ) ) ) ),
    inference(cnf,[status(esa)],[25]) ).

thf(44,plain,
    ! [D: $i > $o,C: $i > $o,B: $i,A: $i] :
      ( ( C @ B )
      | ( D @ B )
      | ~ ( in @ B
          @ ( dsetconstr @ A
            @ ^ [E: $i] :
                ( ( C @ E )
                | ( D @ E ) ) ) ) ),
    inference(simp,[status(thm)],[43]) ).

thf(8,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( kpair @ A @ B )
       != ( kpair @ C @ D ) )
      | ( A = C ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(15,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( kpair @ A @ B )
       != ( kpair @ C @ D ) )
      | ( A = C ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(16,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( kpair @ A @ B )
       != ( kpair @ C @ D ) )
      | ( A = C ) ),
    inference(simp,[status(thm)],[15]) ).

thf(11,plain,
    in @ sk4 @ sk1,
    inference(cnf,[status(esa)],[4]) ).

thf(67,plain,
    ( ( kpair @ sk4 @ sk5 )
    = ( kpair @ sk8 @ sk9 ) ),
    inference(cnf,[status(esa)],[64]) ).

thf(71,plain,
    ( ( kpair @ sk8 @ sk9 )
    = ( kpair @ sk4 @ sk5 ) ),
    inference(lifteq,[status(thm)],[67]) ).

thf(86,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk6 @ A @ ( kpair @ sk4 @ sk5 ) )
        = B )
      | ( ( kpair @ sk8 @ sk9 )
       != ( kpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[71,14]) ).

thf(87,plain,
    ( ( sk6 @ sk8 @ ( kpair @ sk4 @ sk5 ) )
    = sk9 ),
    inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( sk8 )),bind(B,$thf( sk9 ))]]) ).

thf(21,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( ( in @ sk4 @ sk1 )
       != ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,10]) ).

thf(36,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( sk4 != C )
      | ( ( dsetconstr @ A @ B )
       != sk1 ) ),
    inference(simp,[status(thm)],[21]) ).

thf(39,plain,
    ! [B: $i > $o,A: $i] :
      ( ( B @ sk4 )
      | ( ( dsetconstr @ A @ B )
       != sk1 ) ),
    inference(simp,[status(thm)],[36]) ).

thf(325,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( ( dsetconstr @ A @ B )
       != sk1 )
      | ( ( B @ sk4 )
       != ( in @ sk4
          @ ( dsetconstr @ C
            @ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[39,32]) ).

thf(335,plain,
    ! [B: $i > $i,A: $i] :
      ( ( dsetconstr @ A
        @ ^ [C: $i] :
            ( in @ C
            @ ( dsetconstr @ ( B @ C )
              @ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) )
     != sk1 ),
    inference(pre_uni,[status(thm)],[325:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ E @ ( dsetconstr @ ( F @ E ) @ ^ [F: $i] : ( sk3 @ F @ sk5 ) ) ) )),bind(C,$thf( F @ sk4 ))]]) ).

thf(354,plain,
    ! [B: $i > $i,A: $i] :
      ( ( dsetconstr @ A
        @ ^ [C: $i] :
            ( in @ C
            @ ( dsetconstr @ ( B @ C )
              @ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) )
     != sk1 ),
    inference(simp,[status(thm)],[335]) ).

thf(50,plain,
    ! [A: $i] :
      ( ( in @ sk5 @ sk2 )
     != ( in @ sk4
        @ ( dsetconstr @ A
          @ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6,32]) ).

thf(56,plain,
    ! [A: $i] :
      ( ( sk5 != sk4 )
      | ( ( dsetconstr @ A
          @ ^ [B: $i] : ( sk3 @ B @ sk5 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[50]) ).

thf(145,plain,
    ! [B: $i,A: $i] :
      ( ( in @ sk4 @ sk1 )
     != ( in @ B
        @ ( dsetconstr @ A
          @ ^ [C: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[11,46]) ).

thf(152,plain,
    ! [B: $i,A: $i] :
      ( ( sk4 != B )
      | ( ( dsetconstr @ A
          @ ^ [C: $i] : $false )
       != sk1 ) ),
    inference(simp,[status(thm)],[145]) ).

thf(160,plain,
    ! [A: $i] :
      ( ( dsetconstr @ A
        @ ^ [B: $i] : $false )
     != sk1 ),
    inference(simp,[status(thm)],[152]) ).

thf(70,plain,
    in @ sk8 @ sk1,
    inference(cnf,[status(esa)],[64]) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ( sk7 @ A @ ( kpair @ B @ A ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(kpair),[sk7])]) ).

thf(123,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk7 @ A @ ( kpair @ sk4 @ sk5 ) )
        = B )
      | ( ( kpair @ sk8 @ sk9 )
       != ( kpair @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[71,17]) ).

thf(124,plain,
    ( ( sk7 @ sk9 @ ( kpair @ sk4 @ sk5 ) )
    = sk8 ),
    inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( sk9 )),bind(B,$thf( sk8 ))]]) ).

thf(75,plain,
    ! [A: $i] :
      ( ( in @ sk9 @ sk2 )
     != ( in @ sk4
        @ ( dsetconstr @ A
          @ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[69,32]) ).

thf(77,plain,
    ! [A: $i] :
      ( ( sk9 != sk4 )
      | ( ( dsetconstr @ A
          @ ^ [B: $i] : ( sk3 @ B @ sk5 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[75]) ).

thf(68,plain,
    sk3 @ sk8 @ sk9,
    inference(cnf,[status(esa)],[64]) ).

thf(72,plain,
    ( ( sk3 @ sk8 @ sk9 )
   != ( sk3 @ sk4 @ sk5 ) ),
    inference(paramod_ordered,[status(thm)],[68,5]) ).

thf(73,plain,
    ( ( sk8 != sk4 )
    | ( sk9 != sk5 ) ),
    inference(simp,[status(thm)],[72]) ).

thf(324,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( ( dsetconstr @ A @ B )
       != sk1 )
      | ( ( B @ sk4 )
       != ( in @ sk5 @ ( dsetconstr @ C @ ( sk3 @ sk4 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[39,33]) ).

thf(343,plain,
    ! [B: $i > $i,A: $i] :
      ( ( dsetconstr @ A
        @ ^ [C: $i] : ( in @ sk5 @ ( dsetconstr @ ( B @ C ) @ ( sk3 @ C ) ) ) )
     != sk1 ),
    inference(pre_uni,[status(thm)],[324:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ sk5 @ ( dsetconstr @ ( F @ E ) @ ( sk3 @ E ) ) ) )),bind(C,$thf( F @ sk4 ))]]) ).

thf(360,plain,
    ! [B: $i > $i,A: $i] :
      ( ( dsetconstr @ A
        @ ^ [C: $i] : ( in @ sk5 @ ( dsetconstr @ ( B @ C ) @ ( sk3 @ C ) ) ) )
     != sk1 ),
    inference(simp,[status(thm)],[343]) ).

thf(140,plain,
    ! [B: $i,A: $i] :
      ( ( in @ sk9 @ sk2 )
     != ( in @ B
        @ ( dsetconstr @ A
          @ ^ [C: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[69,46]) ).

thf(151,plain,
    ! [B: $i,A: $i] :
      ( ( sk9 != B )
      | ( ( dsetconstr @ A
          @ ^ [C: $i] : $false )
       != sk2 ) ),
    inference(simp,[status(thm)],[140]) ).

thf(159,plain,
    ! [A: $i] :
      ( ( dsetconstr @ A
        @ ^ [B: $i] : $false )
     != sk2 ),
    inference(simp,[status(thm)],[151]) ).

thf(22,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( ( B @ C )
       != ( ~ ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[10]) ).

thf(30,plain,
    ! [A: $i] :
      ~ ( in
        @ ( dsetconstr @ A
          @ ^ [B: $i] :
              ~ ( in @ B @ B ) )
        @ ( dsetconstr @ A
          @ ^ [B: $i] :
              ~ ( in @ B @ B ) ) ),
    inference(pre_uni,[status(thm)],[22:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( in @ D @ D ) )),bind(C,$thf( dsetconstr @ A @ ^ [D: $i] : ~ ( in @ D @ D ) ))]]) ).

thf(368,plain,
    ! [D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( ( B @ C )
       != ( in
          @ ( dsetconstr @ D
            @ ^ [E: $i] :
                ~ ( in @ E @ E ) )
          @ ( dsetconstr @ D
            @ ^ [E: $i] :
                ~ ( in @ E @ E ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10,30]) ).

thf(383,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] :
              ~ ( in @ C @ C ) )
        @ ( dsetconstr @ A
          @ ^ [C: $i] : ( in @ C @ C ) ) ),
    inference(pre_uni,[status(thm)],[368:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ E @ E ) )),bind(C,$thf( dsetconstr @ D @ ^ [E: $i] : ~ ( in @ E @ E ) )),bind(D,$thf( D ))]]) ).

thf(391,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] :
              ~ ( in @ C @ C ) )
        @ ( dsetconstr @ A
          @ ^ [C: $i] : ( in @ C @ C ) ) ),
    inference(simp,[status(thm)],[383]) ).

thf(197,plain,
    ! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i,A: $i] :
      ( ( D @ B )
      | ( E @ B )
      | ( C @ B )
      | ~ ( in @ B
          @ ( dsetconstr @ A
            @ ^ [F: $i] :
                ( ( D @ F )
                | ( E @ F )
                | ( C @ F ) ) ) ) ),
    inference(prim_subst,[status(thm)],[44:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [G: $i] : ( ( E @ G ) | ( F @ G ) ) ))]]) ).

thf(261,plain,
    ! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i,A: $i] :
      ( ~ ( in @ B
          @ ( dsetconstr @ A
            @ ^ [F: $i] :
                ( ( D @ F )
                | ( E @ F )
                | ( C @ F ) ) ) )
      | ( C @ B )
      | ( D @ B )
      | ( E @ B ) ),
    inference(cnf,[status(esa)],[197]) ).

thf(262,plain,
    ! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i,A: $i] :
      ( ~ ( in @ B
          @ ( dsetconstr @ A
            @ ^ [F: $i] :
                ( ( D @ F )
                | ( E @ F )
                | ( C @ F ) ) ) )
      | ( C @ B )
      | ( D @ B )
      | ( E @ B ) ),
    inference(simp,[status(thm)],[261]) ).

thf(51,plain,
    ! [A: $i] :
      ( ( in @ sk4
        @ ( dsetconstr @ A
          @ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) )
     != ( in @ sk4 @ sk1 ) ),
    inference(paramod_ordered,[status(thm)],[11,32]) ).

thf(57,plain,
    ! [A: $i] :
      ( ( sk4 != sk4 )
      | ( ( dsetconstr @ A
          @ ^ [B: $i] : ( sk3 @ B @ sk5 ) )
       != sk1 ) ),
    inference(simp,[status(thm)],[51]) ).

thf(62,plain,
    ! [A: $i] :
      ( ( dsetconstr @ A
        @ ^ [B: $i] : ( sk3 @ B @ sk5 ) )
     != sk1 ),
    inference(simp,[status(thm)],[57]) ).

thf(992,plain,
    $false,
    inference(e,[status(thm)],[69,5,37,14,46,121,6,757,13,44,3,16,11,87,354,10,56,160,70,33,124,77,73,360,32,17,159,71,391,7,39,262,30,47,68,62]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEU668^2 : TPTP v8.2.0. Released v3.7.0.
% 0.08/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n015.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sun May 19 17:38:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.99/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.16/0.98  % [INFO] 	 Parsing done (111ms). 
% 1.16/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.53/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.71/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.71/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.87/1.28  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.87/1.28  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.87/1.28  % [INFO] 	 Type checking passed. 
% 1.87/1.28  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 11.48/3.39  % External prover 'e' found a proof!
% 11.48/3.39  % [INFO] 	 Killing All external provers ... 
% 12.02/3.39  % Time passed: 2862ms (effective reasoning time: 2402ms)
% 12.02/3.39  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 12.02/3.39  % Axioms used in derivation (0): 
% 12.02/3.39  % No. of inferences in proof: 81
% 12.02/3.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2862 ms resp. 2402 ms w/o parsing
% 12.02/3.44  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.02/3.44  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------